may thanh giup em voi!!
(x-1)(x+1)(x+2)
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1.: Áp dụng BĐT Cauchy-Schwarz cho 3 số dương
\(a+b+c\ge3\sqrt[3]{abc};\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge3\sqrt[3]{\frac{1}{abc}}\)
\(\Rightarrow\left(a+b+c\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge3\sqrt[3]{abc}.3\sqrt[3]{\frac{1}{abc}}=9\)
\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
Có: \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\)
\(\Rightarrow x+1=0\)
\(\Rightarrow x=-1\)
\(\frac{x-1}{5}=\frac{y+4}{-3}=\frac{z-2}{1}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x-1}{5}=\frac{y+4}{-3}=\frac{z-2}{1}=\frac{\left(x-1\right)-5\left(y+4\right)+\left(z-2\right)}{5-5.\left(-3\right)+1}=\frac{-5}{21}\)
\(\Leftrightarrow\hept{\begin{cases}x-1=-\frac{5}{21}.5\\y+4=\frac{-5}{21}.\left(-3\right)\\z-2=-\frac{5}{21}.1\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-\frac{4}{21}\\y=\frac{-23}{7}\\z=\frac{37}{21}\end{cases}}\)
\(\left(xy+1\right)^2-\left(x-y\right)^2=\left(xy+1+x-y\right)\left(xy+1-x+y\right)\)
\(=x^2y^2+xy-x^2y+xy^2+xy+1-x+y+x^2y+x-x^2+xy-xy^2-y+xy-y^2\)
\(=x^2y^2+2xy-x^2-y^2+1\)
a) \(a^5+a^3-a^2-1\)
\(=a^5+a^4+a^3+a^3+a^2+a-a^4-a^3-a^2-a^2-a-1\)
\(=a^3\left(a^2+a+1\right)+a\left(a^2+a+1\right)-a^2\left(a^2+a+1\right)-\left(a^2+a+1\right)\)
\(=\left(a^3+a-a^2-1\right)\left(a^2+a+1\right)\)
\(=\left[\left(a^3-1\right)-a\left(a-1\right)\right]\left(a^2+a+1\right)\)
\(=\left[\left(a-1\right)\left(a^2+a+1\right)-a\left(a-1\right)\right]\left(a^2+a+1\right)\)
\(=\left(a-1\right)\left(a^2+a+1-a\right)\left(a^2+a+1\right)\)
\(=\left(a-1\right)\left(a^2+1\right)\left(a^2+a+1\right)\)
b) \(27a^2b^2-18ab+3\)
\(=3\left(9a^2b^2-6ab+1\right)\)
\(=3\left(3ab-1\right)^2\)
c) \(4-x^2-2xy-y^2\)
\(=4-\left(x+y\right)^2\)
\(=\left(2-x-y\right)\left(2+x+y\right)\)
Đề là sao ? =)
Bạn đưa đề vậy giúp sao đc
Hok tốt :)
de chi the thi